Question 28457: solve: 2^(x+1) * 8^(-x)=4
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! solve: 2^(x+1) * 8^(-x)=4
2^(x+1) X 8^(-x)=4
2^(x+1) X(2^3)^(-x) = 2^2
2^(x+1) X (2^(-3x)) = 2^2
2^[(x+1)+(-3x)] = 2^2
2^(x+1-3x) = 2^2
2^(1-2x) = 2^2
(1-2x) = 2 (using the rule: bases are the same, so powers are equal)
1-2 = 2x
-1 = 2x
x = (-1/2)
Answer: x = (-1/2)
Verification: Putting x = (-1/2)in 2^(x+1) X 8^(-x)=4
LHS = 2^(x+1) X 8^(-x)
=2^(-1/2+1) X 8^(1/2)
=2^(1/2)X 2^(3/2) (as 8 = 2^3)
= 2^(1/2+3/2)
=2^2
4 =RHS which is correct
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